TY - GEN AU - Szücs, Mátyás AU - Fülöp, Tamás TI - Exact analytical solution for the non-selfadjoint problem of Maxwell–Cattaneo–Vernotte heat conduction with heat-transfer boundary condition PY - 2026 PG - 35 UR - https://m2.mtmt.hu/api/publication/37444899 ID - 37444899 LA - English DB - MTMT ER - TY - JOUR AU - Fülöp, Tamás AU - Szücs, Mátyás AU - Takács, Donát M. TI - GENERIC-motivated extended symplectic numerical methods for dissipative mechanical systems: A concrete example and general messages JF - JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS J2 - JCAM VL - 20 PY - 2025 IS - 1 SP - 3 EP - 33 PG - 31 SN - 1586-2070 DO - 10.32973/jcam.2025.001 UR - https://m2.mtmt.hu/api/publication/36074073 ID - 36074073 AB - The GENERIC (General Equation for the Non-Equilibrium Reversible-Irreversible Coupling) framework is used, first, to present the irreversible thermodynamical formulation of the Rayleigh potential, and, subsequently, to realize the dynamical equations of motion of a supercritical van der Waals fluid separated from the environment by a movable rigid piston. Motivated by the latter, a quasi-symplectic generalization of the symplectic Euler finite-difference numerical scheme is introduced for this setup. A remarkable advantage over the explicit Euler scheme regarding artificial numerical antidissipation is illustrated. The possibility of controlled artificial numerical damping is addressed. The quasi-symplectic scheme is proven to enable efficient simulation of the considerably nonlinear and sensitive processes near the liquid-vapour critical point. A numerically feasible quantitative measure of nonlinearity of time-dependent processes is introduced and applied. LA - English DB - MTMT ER - TY - JOUR AU - Fülöp, Tamás TI - The Kluitenberg–Verhás model of viscoelasticity and its irreversible thermodynamical consistency via rheological energy JF - JOURNAL OF COMPUTATIONAL AND APPLIED MECHANICS J2 - JCAM VL - 20 PY - 2025 IS - 2 SP - 93 EP - 117 PG - 25 SN - 1586-2070 DO - 10.32973/jcam.2025.004 UR - https://m2.mtmt.hu/api/publication/37071195 ID - 37071195 AB - Rocks and plastics are two examples of classes of materials where theKluitenberg–Verh´as model of viscoelasticity has proved adequate for describing the observedmechanical behaviour. This model cannot be interpreted as a generalized Maxwell model,and requires in fact a novel rheological circuit element beyond the spring and the dashpot.Moreover, its thermodynamical consistency leads to nontrivial inequality conditions on themodel coefficients, ignoring which would lead to violation of the second law of thermodynamics and would thus be a principal source of instability of numerical solutions. The presentpaper explores the role of the rheological energy contribution embedded in the Kluitenberg–Verh´as model, in a didactic and application-oriented way. The explicit meaning of theinvolved irreversible thermodynamical additional state variable – internal degree of freedom– is identified. Neither thermal expansion nor heat conduction is neglected, enhancing theapplicability of the constructed framework. LA - English DB - MTMT ER - TY - JOUR AU - Takács, Donát M. AU - Fülöp, Tamás TI - Improving the accuracy of the Newmark method through backward error analysis JF - COMPUTATIONAL MECHANICS J2 - COMPUT MECH VL - 75 PY - 2025 IS - 5 SP - 1585 EP - 1606 PG - 22 SN - 0178-7675 DO - 10.1007/s00466-024-02580-3 UR - https://m2.mtmt.hu/api/publication/34726196 ID - 34726196 AB - We use backward error analysis for differential equations to obtain modified or distorted equations describing the behaviour of the Newmark scheme applied to the transient structural dynamics equation. Based on the newly derived distorted equations, we give expressions for the numerically or algorithmically distorted stiffness and damping matrices of a system simulated using the Newmark scheme. Using these results, we show how to construct compensation terms from the original parameters of the system, which improve the performance of Newmark simulations. The required compensation terms turn out to be slight modifications to the original system parameters (e.g. the damping or stiffness matrices), and can be applied without changing the time step or modifying the scheme itself. Two such compensations are given: one eliminates numerical damping, while the other achieves fourth-order accurate calculations using the traditionally second-order Newmark method. The performance of both compensation methods is evaluated numerically to demonstrate their validity, and they are compared to the uncompensated Newmark method, the generalized-α method and the 4th-order Runge–Kutta scheme. © The Author(s) 2024. LA - English DB - MTMT ER - TY - JOUR AU - Takács, Donát M. AU - Fülöp, Tamás AU - Kovács, Róbert Sándor AU - Szücs, Mátyás TI - The piston effect in supercritical fluids investigated via a reversible–irreversible vector field splitting-based explicit time integration scheme JF - PHYSICS OF FLUIDS J2 - PHYS FLUIDS VL - 37 PY - 2025 IS - 7 PG - 19 SN - 1070-6631 DO - 10.1063/5.0271333 UR - https://m2.mtmt.hu/api/publication/36161803 ID - 36161803 N1 - Funding Agency and Grant Number: Ministry of Culture and Innovation of Hungary from the National Research, Development and Innovation Fund [TKP-6-6/PALY-2021]; Sustainable Development and Technologies National Programme of the Hungarian Academy of Sciences (FFT NP FTA); Hungarian Scientific Research Fund [NKKP-Advanced150038]; Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences; University Researcher Scholarship Program (EKOP) of the National Research, Development and Innovation Office - Ministry of Culture and Innovation Funding text: Project No. TKP-6-6/PALY-2021 has been implemented withthe support provided by the Ministry of Culture and Innovation ofHungary from the National Research, Development and InnovationFund, financed under the TKP2021-NVA funding scheme. Theresearch was partially supported by the Sustainable Development and Technologies National Programme of the Hungarian Academy of Sciences (FFT NP FTA) and by the Hungarian Scientific Research Fund under Grant agreement No. NKKP-Advanced150038 (Sz.M.). The research was supported by the Janos Bolyai Research Scholarship of the Hungarian Academy of Sciences (K.R.).The work was supported by the University Researcher Scholarship Program (EKOP) of the National Research, Development and Innovation Office, which is also supported by the Ministry of Culture and Innovation (T.D.). We also acknowledge KIFU(Governmental Agency for IT Development, Hungary) for grantingus access to the Komondor HPC facility based in Hungary. AB - In the vicinity of the liquid–vapor critical point, supercritical fluids behave strongly compressible and, in parallel, thermophysical properties have strong state dependence. These lead to various peculiar phenomena, one of which is the piston effect where a sudden heating induces a mechanical pulse. The coupling between thermal and mechanical processes, in the linear approximation, yields a non-trivially rich thermoacoustics. The numerous applications of supercritical fluids raise the need for a reliable yet fast and efficient numerical solution for thermoacoustic time and space dependence in this sensitive domain. Here, we present a second-order accurate, fully explicit staggered space–time grid finite difference method for such coupled linear thermoacoustic problems. Time integration is based on the splitting of the state space vector field representing the interactions that affect the dynamics into reversible and irreversible parts, which splitting procedure leads to decoupled wave and heat equations. The former is a hyperbolic partial differential equation, while the latter is a parabolic one; therefore, different time integration algorithms must be amalgamated to obtain a reliable, dispersion error-free, and dissipation error-free numerical solution. Finally, the thermoacoustic approximation of the supercritical piston effect is investigated via the developed method. LA - English DB - MTMT ER - TY - JOUR AU - Takács, Donát M. AU - Fülöp, Tamás TI - Improving Discrete Numerical Methods for Dynamics Using Continuous Mathematical Tools JF - ADVANCES IN SCIENCE AND TECHNOLOGY J2 - ADV SCI TECHNOL VL - 165 PY - 2025 SP - 21 EP - 30 PG - 10 SN - 1662-8969 DO - 10.4028/p-11TtO6 UR - https://m2.mtmt.hu/api/publication/36178057 ID - 36178057 N1 - Utánközlése: 36227399. AB - We briefly review backward error analysis as a useful mathematical technique for improving numerical methods used for solving ordinary differential equations describing dynamical systems. Then, we show how backward error analysis-based compensation, an approach recently introduced by the authors, can be applied to the second-order Newmark method for eliminating numerical damping and achieving fourth-order convergence. The presented improvements only require modifying the physical parameters of the system and the excitation, while the Newmark method is left intact. We compare the performance of the resulting improvements with that of several other numerical methods, including a novel partitioned method based on local extrapolation. LA - English DB - MTMT ER - TY - JOUR AU - Takács, Donát M. AU - Fülöp, Tamás TI - On the coordinate system-dependence of the accuracy of symplectic numerical methods JF - JOURNAL OF NUMERICAL ANALYSIS AND APPROXIMATION THEORY J2 - J NUMER ANA. APPROX THEORY VL - 54 PY - 2025 IS - 2 SP - 315 EP - 344 PG - 30 SN - 2457-6794 DO - 10.33993/jnaat542-1577 UR - https://m2.mtmt.hu/api/publication/36214178 ID - 36214178 N1 - The work of this author has been supported by the EKÖP-24-3-BME-247 grant of the National Research, Development and Innovation Office under the University Researcher Scholarship Program (EKÖP) AB - Symplectic numerical methods have become a widely-used choice for the accurate simulation of Hamiltonian systems in various fields, including celestial mechanics, molecular dynamics and robotics. Even though their characteristics are well-understood mathematically, relatively little attention has been paid in general to the practical aspect of how the choice of coordinates affects the accuracy of the numerical results, even though the consequences can be computationally significant. The present article aims to fill this gap by giving a systematic overview of how coordinate transformations can influence the results of simulations performed using symplectic methods. We give a derivation for the non-invariance of the modified Hamiltonian of symplectic methods under coordinate transformations, as well as a sufficient condition for the non-preservation of a first integral corresponding to a cyclic coordinate for the symplectic Euler method. We also consider the possibility of finding order-compensating coordinate transformations that improve the order of accuracy of a numerical method. Various numerical examples are presented throughout. LA - English DB - MTMT ER - TY - CHAP AU - Takács, Donát M. AU - Fülöp, Tamás ED - Csüllög, Mihály ED - Mankovits, Tamás TI - Improving Discrete Numerical Methods for Dynamics Using Continuous Mathematical Tools T2 - The 10th International Scientific Conference on Advances in Mechanical Engineering (ISCAME) PB - Trans Tech Publications CY - Bäch SN - 9783036406107 PY - 2025 SP - 235 EP - 244 PG - 10 UR - https://m2.mtmt.hu/api/publication/36227399 ID - 36227399 N1 - 36178057 utánközlése. AB - We briefly review backward error analysis as a useful mathematical technique for improving numerical methods used for solving ordinary differential equations describing dynamical systems. Then, we show how backward error analysis-based compensation, an approach recently introduced by the authors, can be applied to the second-order Newmark method for eliminating numerical damping and achieving fourth-order convergence. The presented improvements only require modifying the physical parameters of the system and the excitation, while the Newmark method is left intact. We compare the performance of the resulting improvements with that of several other numerical methods, including a novel partitioned method based on local extrapolation. LA - English DB - MTMT ER - TY - JOUR AU - Takács, Donát M. AU - Fülöp, Tamás TI - Szimplektikus numerikus módszerek és műszaki alkalmazásuk néhány gyakorlati szempontja [Symplectic numerical methods and some practical aspects of their application for engineering problems] JF - MULTIDISZCIPLINÁRIS TUDOMÁNYOK: A MISKOLCI EGYETEM KÖZLEMÉNYE J2 - MULTIDISZCIPLINÁRIS TUDOMÁNYOK VL - 14 PY - 2024 IS - 4 SP - 3 EP - 23 PG - 21 SN - 2062-9737 DO - 10.35925/j.multi.2024.4.1 UR - https://m2.mtmt.hu/api/publication/34259085 ID - 34259085 LA - Hungarian DB - MTMT ER - TY - JOUR AU - Takács, Donát M. AU - Pozsár, Áron AU - Fülöp, Tamás TI - Thermodynamically extended symplectic numerical simulation of viscoelastic, thermal expansion and heat conduction phenomena in solids JF - CONTINUUM MECHANICS AND THERMODYNAMICS J2 - CONTINUUM MECH THERM VL - 36 PY - 2024 SP - 525 EP - 538 PG - 14 SN - 0935-1175 DO - 10.1007/s00161-024-01280-w UR - https://m2.mtmt.hu/api/publication/34575282 ID - 34575282 AB - Symplectic numerical schemes for reversible dynamical systems predict the solution reliably over large times as well, and are a good starting point for extension to schemes for simulating irreversible situations like viscoelastic wave propagation and heat conduction coupled via thermal expansion occuring in rocks, plastics, biological samples etc. Dissipation error (artificial nonpreservation of energies and amplitudes) of the numerical solution should be as small as possible since it should not be confused with the real dissipation occurring in the irreversible system. In addition, the other well-known numerical artefact, dispersion error (artificial oscillations emerging at sharp changes), should also be minimal to avoid confusion with the true wavy behavior. The continuum thermodynamical aspects (respect for balances with fluxes, systematic constitutive relationships between intensive quantities and fluxes, the second law of thermodynamics with positive definite entropy production, and the spacetime-based kinematic viewpoint) prove valuable for obtaining such extended schemes and for monitoring the solutions. Generalizing earlier works in this direction, here, we establish and investigate such a numerical scheme for one-dimensional viscoelastic wave propagation in the presence of heat conduction coupled via thermal expansion, demonstrating long-term reliability and the applicability of thermodynamics-based quantities in supervising the quality of the solution. LA - English DB - MTMT ER -